You most certainly can. Obviously you just have to fry them for longer until completely cooked through.
Here's an example recipe that does it this way
http://www.foodnetwork.com/recipes/nigella-lawson/tarragon-chicken-recipe-1923007 Notice, though, that it involves adding some white wine after 5 minutes and that helps to keep the breasts moist - they do have a tendency to dry out because there is so little fat in them.
They're cooked and safe to eat when they have gone white all the way through. HOW you cook them so that happens doesn't matter!